Vance weighs 250 pounds and is losing 5 pounds each month. Phillip weighs 200 pounds and is gaining 4 pounds each month. Write an equation that can be used to find m, the
number of months it will take for Vance to weigh the same as Phil?
Drag and drop the appropriate variable or number into each box.
250
200
5
4
9
1
m

250-5m=200+4m ; 5.56 months

Step-by-step explanation:

Let's start this question by writing two expressions that depict the situation.

Vance: 250-5m

This simply means that Vance currently weighs 250 pounds, and every month he is losing 5 pounds. (m=number of months)

Phillip: 200+4m

This is essentially the same thing. Phillips starting weight is 200, but here we use an addition sign because he is gaining 4 pounds every month as opposed to losing it.

To find the number of months it'll take for them to weigh the same, we just need to equate the values and solve for m.

Our equation would then be:

250-5m=200+4m

Let's solve the equation by bringing the variables to one side and the numbers to the other.

250-5m=200+4m

Subtract 4m from both sides

250-5m-4m=200+4m-4m

250-9m=200

Subtract 250 from both sides

250-250-9m=200-250

-9m=-50

Divide both sides by -9

m=5.556

So it will take about 5 months and a half to weigh the same.